英文标题：
《Invest or Exit? Optimal Decisions in the Face of a Declining Profit
Stream》
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作者：
H. Dharma Kwon
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最新提交年份：
2019
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英文摘要：
Even in the face of deteriorating and highly volatile demand, firms often invest in, rather than discard, aging technologies. In order to study this phenomenon, we model the firm\'s profit stream as a Brownian motion with negative drift. At each point in time, the firm can continue operations, or it can stop and exit the project. In addition, there is a one-time option to make an investment which boosts the project\'s profit rate. Using stochastic analysis, we show that the optimal policy always exists and that it is characterized by three thresholds. There are investment and exit thresholds before investment, and there is a threshold for exit after investment. We also effect a comparative statics analysis of the thresholds with respect to the drift and the volatility of the Brownian motion. When the profit boost upon investment is sufficiently large, we find a novel result: the investment threshold decreases in volatility.
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中文摘要：
即使面对不断恶化和高度波动的需求，企业也往往投资于老化的技术，而不是丢弃。为了研究这一现象，我们将企业的利润流建模为具有负漂移的布朗运动。在每个时间点，公司都可以继续运营，也可以停止并退出项目。此外，还有一种一次性投资选择，可以提高项目的利润率。利用随机分析，我们证明了最优策略总是存在的，并且具有三个阈值的特征。投资前有投资和退出门槛，投资后有退出门槛。我们还对布朗运动的漂移和波动性阈值进行了比较静态分析。当投资带来的利润增长足够大时，我们发现了一个新的结果：投资阈值的波动性降低。
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分类信息：

一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Economics 经济学
二级分类：General Economics 一般经济学
分类描述：General methodological, applied, and empirical contributions to economics.
对经济学的一般方法、应用和经验贡献。
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一级分类：Quantitative Finance 数量金融学
二级分类：Economics 经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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